In tropical Townsville, the hosts trailed 21-7 at the break before showing steely nerve with a sensational second-half comeback, capped by Angus Bell’s converted try at the death.
Joseph-Aukuso Suaalii bagged a brace and Nic White also dotted down to cancel out tries from Santiago Carreras and Bautista Delguy.
Australia had the option to level the scores when down 24-21 with a minute to go after being awarded a penalty, but never-say-die skipper Harry Wilson opted to go for touch and the win.
It left them with two victories from three in the southern hemisphere tournament, ahead of a return leg against the Pumas in Sydney next week.
One of those wins was a shock bonus-point upset of world champions South Africa in Johannesburg, which came on the back of beating the British and Irish Lions as momentum builds under Joe Schmidt.
Every win is crucial at the moment for world rankings points ahead of December’s draw for the 2027 World Cup, which Australia host.
The top-ranked nations, come December, will head each of the six groups, meaning they potentially avoid some of the big guns in the tournament pool stages.
Argentina are currently ranked seven to Australia’s six and the defeat will see them slide further behind. (AFP)
